Pixels artifacts when rendering glass BSDF with Cycles
Those bright pixels you are seeing are Caustics - the stray rays of light that pass through or reflect from a refractive or reflective surface. Given enough samples they will form a meaningful image of the light that passes through your mesh - but they typically require a lot of samples for this - see @bertmoog's answer to Will increasing samples reduce fireflies? for a really good example of different numbers of samples and the effect on the quality of caustics.

An easy way to avoid them is to disable caustics in the Render Light Path settings :



Another option is to increase the Filter Glossy value on the same panel. This will effectively 'smear out' the single bright dots of caustic to produce more pleasing results with considerably fewer samples - at the expense of the accuracy of the caustics. Interestingly, at Blender version 2.79 this value defaulted to 0.0 (pinpoint caustics) whereas at 2.79.5+ (and 2.8) it defaults to 1.0 which produces a more generally acceptable rendering of caustics 'out of the box'. Adjust the value lower for sharper caustics and higher for rendering with fewer samples.